Gaussian Process regression models are used to determine functions that model known data. The known data can be, for example, discrete elevation measurements over a certain area. The model would then provide a means of inferring values for intermediate points that were not measured, called test points.
In a large scale environment like an open-cut mine spatial modelling of geography and geology can have many uses in planning, analysis and operations within the environment. In the case of automated mining, a geographical model or terrain map can be used to guide robotic vehicles, whilst an in-ground geological model of the ore body may be used to determine drilling and blasting operations.
A digital representation of the operating environment in the form of a spatial model is typically generated from sensor measurements which provide a sample of the actual environmental variable being modelled (e.g. elevation in the case of a terrain map, or ore grade in the case of in-ground ore body modelling) at various spatially distinct locations within the operating environment. The measured sample data is then treated in some manner such as by interpolation to determine information about the environment in locations other than those actually measured. Some of the challenges posed by this task include dealing with the issues of uncertainty, incompleteness and handling potentially large measurement data sets.
Gaussian Processes (GPs) are stochastic processes based on the normal (Gaussian) distribution and can be used to good effect as a powerful nonparametric learning technique for modelling. Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, and is sometimes referred to as “Kriging”.
Whilst Gaussian processes are a useful and powerful tool for regression in supervised machine learning they are regarded as a computationally expensive technique, which is particularly disadvantageous in the treatment of large measurement data sets. The computational expense is primarily brought on by the need to invert a large covariance matrix during the inference procedure. For problems with thousands of observations, exact inference in normal Gaussian processes is intractable and approximation algorithms are required.